This specification relates to computer-aided design (CAD) applications and, in particular, to converting T-spline models to trim-free T-spline models.
Computer-aided design (CAD) can be used to model surfaces that resemble smooth, real-world objects. For example, a boundary representation (B-rep) CAD model typically consists of a collection of surfaces that are augmented using trim curves and that are organized topologically in boundary loops. The B-rep CAD model includes additional geometrical and topological information that represents surface domains in the CAD model. Trim curves can be created using various operations, including, for example, sketching, intersections, and imprinting. Further, trim curves can be defined by complicated geometry that is often more involved mathematically and is more computationally expensive to define than the surfaces that are supporting the curves.
When processing a B-rep CAD model, a downstream algorithm typically has to account for all of the trim curves and boundary loops when determining which regions of the surfaces are included in the model. This added complexity makes some operations, including, for example, direct modeling and simulation, more difficult. As a result, for many downstream operations, such as analysis, a B-rep CAD model is first converted into a simpler trim-free representation, e.g., a polygonal mesh (generally a triangular mesh), which does not require trim curves and boundary loops to define the extent of the model. However, use of polygonal meshes generally results in a loss of precision, sharp features, and important high order geometrical infomiation (e.g., the curvature tensor), and requires a high number of elements. Thus, polygonal meshes are generally a poor substitute for the original surface geometry of a model. Use of polygonal meshes in downstream operations typically results in suboptimal downstream results and, sometimes, outright failures.